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Concerning the construction of taxicab ellipses. (English) Zbl 1122.51012

The authors consider the problem of constructing ellipses in the plane endowed with the taxicab metric. After fixing two arbitrary points, there are described explicitly (by means of equalities and inequalities) planar regions \(G_i\), \(i=1,2,3,4\), characterized by the property that a taxicab ellipse contains the given points and a third one if and only if the third point lies in the union of the regions \(G_1\) through \(G_4\).

MSC:

51K05 General theory of distance geometry
51M05 Euclidean geometries (general) and generalizations
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